Discontinuous failure in micropolar elastic-degrading models

The present paper investigates the phenomenon of discontinuous failure (or localization) in elastic-degrading micropolar media. A recently proposed unified formulation for elastic degradation in micropolar media, defined in terms of secant tensors, loading functions and degradation rules, is used as a starting point for the localization analysis. Well-known concepts on acceleration waves propagation, such as the Maxwell compatibility condition and the Fresnel–Hadamard propagation condition, are derived for the considered material model in order to obtain a proper failure indicator. Peculiar problems are investigated analytically in details, in order to evaluate the effects on the onset of localization of two of the additional material parameters of the micropolar continuum, the Cosserat’s shear modulus and the internal bending length. Numerical simulations with a finite element model are also presented, in order to show the regularization behaviour of the micropolar formulation on the pathological effects due to the localization phenomenon.

Purpose
This paper presents a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having a global and local scale components.
This strategy allows the use of a coarse mesh even when the problem produces complex local phenomena. For this purpose, local problems can be defined where these local phenomena are observed and are solved separately using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution.

Design/methodology/approach
The implementation of the two-scale G/XFEM formulation follows the object-oriented approach presented by the authors in a previous work, where it is possible to combine different kinds of elements and analysis models with the partition of unity enrichment scheme.
Beside the extension of the G/XFEM implementation to enclose the global-local strategy, the imposition of different boundary conditions is also generalized.

Findings
The generalization done for boundary conditions is very important since the global-local approach relies on the boundary information transferring process between the two scales of the analysis. The flexibility for the numerical analysis of the proposed framework is illustrated by several examples. Different analysis models, element formulations and enrichment functions are employed and the accuracy, robustness and computational efficiency are demonstrated.

Originality/value
This work shows a generalize imposition of different boundary conditions for global-local G/XFEM analysis through an object-oriented implementation. This generalization is very important since the global-local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problem simultaneously and solving plate problems using global-local G/XFEM is another contributions of this work.

A computational framework for constitutive modelling

The field of computational constitutive modelling for engineering applications is an active research tread in academia. New advanced models and formulations are constantly proposed. However, when dealing with implementation aspects, often the main concern is to provide a minimal environment to show a certain model and its applications, with implementations made from scratch. Though advanced, usually such implementations lack of generality and are well-suited for a certain numerical method while not compatible with other ones, making it difficult to reuse the code in other contexts. The Object-Oriented Paradigm (OOP) to programming have been widely applied in the last years for the realization of numerous academic numerical simulation softwares, due to its fundamental properties of abstraction, inheritance and polymorphism that allow the creation of programs well-suited for an easy collaboration between developers with expertise in different fields of engineering and mechanics. As showed in this paper, the same properties can be effectively extended also to the constitutive aspects of a model. The application of the OOP to the constitutive modelling of a wide range of materials of engineering interest is investigated, aiming to the creation of a computational framework for constitutive models that is fully independent on the other components of a code and easy to expand.

A computational framework for G/XFEM material nonlinear analysis

The Generalized/eXtended Finite Element Method (G/XFEM) has been developed with the purpose of overcoming some limitations inherent to the Finite Element Method (FEM). Different kinds of functions can be used to enrich the original FEM approximation, building a solution specially tailored to problem. Certain obstacles related to the nonlinear analysis can be mitigated with the use of such strategy and the damage and plasticity fronts can be precisely represented. A FEM computational environment has been previously enclosed the G/XFEM formulation to linear analysis with minimum impact in the code structure and with requirements for extensibility and robustness. An expansion of the G/XFEM implementation to physically nonlinear analysis under the approach of an Unified Framework for constitutive models based on elastic degradation is firstly presented here. The flexibility of the proposed framework is illustrated by several examples with different constitutive models, enrichment functions and analysis models.

An enhanced tensorial formulation for elastic degradation in micropolar continua

In the past, a lot of applications of the micropolar (or Cosserat) continuum theory have been proposed, especially in the field of granular materials analysis and for strain localization problems in elasto-plasticity, due to its regularization properties. In order to make possible the application of the micropolar theory to different constitutive models and to extend its regularization properties also to damage models, in this work a general formulation for elastic degradation based on the micropolar theory is proposed. Such formulation is presented in a unified format, able to enclose different kinds of elasto-plastic, elastic-degrading and damage constitutive models. A peculiar tensor-based representation is introduced, in order to guarantee the conformity with analogous theories based on the classic continuum, in such a way as to make possible the application to the micropolar theory of theoretical and numerical resources already defined for the classic theory. Peculiar micropolar scalar damage models are also proposed, and derived within the new general formulation.

High regularity partition of unity for structural physically non-linear analysis

Meshfree techniques, such as hp-Clouds and Element Free Galerkin Methods, have been used as attractive alternatives to finite element method, due to the flexibility in constructing conforming approximations. These approximations can present high regularity, improving the description of the state variables used in physically non-linear problems. On the other hand, some drawbacks can be highlighted, as the lack of the Kronecker-delta property and numerical integration problems. These drawbacks can be overcome by using a Ck, k arbitrarily large, partition of unity (PoU) function, built over a finite element mesh, but with the approximate characteristic of the meshfree methods. Here, this procedure is for the first time investigated to simulate the non-linear behavior of structures with quasi-brittle materials. The smeared crack model is adopted and numerical results, obtained with different kinds of polynomial enrichments, are compared with the experimental results.

A new solution strategy for the non-linear Implicit Formulation of the Boundary Element Method is presented. Such strategy is based on a decomposition of the strain increment variation vector in two parts: one associated to the cumulative external loads and another associated to the current unbalanced vector, obtained from the difference of the first part and the calculated internal strain field distribution, during the iterative process. This approach makes the algorithm generic enough to deal with different control methods that governs the progression of the non-linear analysis. Also, a unified constitutive modelling framework for a single loading function is used to provide the material constitutive informations required by the solution strategy, which permits the implementation of a very comprehensive series of models in an independent way. However, only local models were treated. To demonstrate the efficiency and versatility of the methodology, some numerical examples are presented.

This paper shows and discusses a generic implementation of the global-local analysis toward generalized finite element method (GFEMgl). This implementation, performed into an academic computational platform, follows the object-oriented approach presented by the authors in a previous work for the standard version of GFEM in which the shape functions of finite elements are hierarchically enriched by analytical functions, according to the problem behavior. In global-local GFEM, however, the enrichment functions are constructed numerically from the solution of a local problem. This strategy allows the use of a coarse mesh even when the problem produces complex stress distributions. On the other hand, a local problem is defined where the stress field presents high gradients and it is discretized using a large number of elements. The results of the local problem are used to enrich the global problem which improves the approximate solution. The great advantage is allowing a well-refined description of the local problem, when necessary, avoiding an overburden for the computation of the global solution. Details of the implementation are presented and important aspects of using this strategy are highlighted in the numerical examples.

A generalized elasto-plastic micro-polar constitutive model

This paper summarizes the implementation of an elasto-plastic constitutive model for a micro-polar continuum in the constitutive models framework of the software INSANE (INteractive Structural ANalysis Environment). Such an implementation is based on the tensorial format of a unified constitutive models formulation, that allows to implement different constitutive models independently on the peculiar numerical method adopted for the solution of the problem. The basic characteristics of the micro-polar continuum model and of the unified formulation of constitutive models are briefly recalled. A generalization of the micro-polar model is then introduced in order to include this model in the existent tensor-based formulation. Finally, an enhanced version of the general closest-point algorithm, ables to manage the generalized micro-polar formulation, is derived. A strain localization problem modeling illustrates the implementation.

Experimental and finite element analysis of bond-slip in reinforced concrete

The modeling of reinforced concrete structures has taken advantage of the increasing progress on Computational Mechanics, in such way that complex phenomena, such as cracking and crushing, creep, reinforcement yielding, steel-concrete bond loss, can be modeled in a reasonable realistic way, using the proper set of numerical and computational resources. Among several options, the ones based on the Finite Element Method (FEM) allow complex analysis simulations of reinforced concrete structures, including the interaction of different nonlinear effects. This paper deals with the nonlinear finite element analysis of the bond-slip between reinforcing steel and concrete, taking into account an experimental study previously performed. The FEM analysis presented uses a combination of resources where the material behavior of concrete is described by the Microplane Constitutive Model, and an embedded reinforcement model is used to represent steel inside the concrete and take into account the effect of bond-slip. The FEM models were created using the INSANE (INteractive Structural ANalysis Environment) computational system, open source software that has a set of FEM tools for nonlinear analysis of reinforced concrete structures. The correlations between numerical-experimentals results and several parameters validate the proposed combination of resources and identifies the significance of various effects on the response.

An object-oriented approach to the Generalized Finite Element Method

The Generalized Finite Element Method (GFEM) is a meshbased approach that can be considered as one instance of the Partition of Unity Method (PUM). The partition of unity is provided by conventional interpolations used in the Finite Element Method (FEM) which are extrinsically enriched by other functions specially chosen for the analyzed problem. The similarities and differences between GFEM and FEM are pointed out here to expand a FEM computational environment. Such environment is an object-oriented system that allows linear and non-linear, static and dynamic structural analysis and has an extense finite element library. The aiming is to enclose the GFEM formulation with a minimum impact in the code structure and meet requirements for extensibility and robustness. The implementation proposed here make it possible to combine different kinds of elements and analysis models with the GFEM enrichment strategies. Numerical examples, for linear analysis, are presented in order to demonstrate the code expansion and to illustrate some of the above mentioned combinations.

The object-oriented design used to implement a self-regular formulation of the boundary element method is presented. The self-regular formulation is implemented to four integral equations: the displacement boundary integral equation, and the Somigliana’s integral identities for displacement, stress and strain. The boundary-layer effect that arises in the classical BEM on the transition from interior to boundary points is eliminated and thus special integration schemes to treat nearly singular integrals become unnecessary. The self-regular formulations lead to very accurate results. Comparisons of displacements, stress and strain obtained from analytical solutions and the numerical results for bidimensional and tridimensional elastostatics problems are presented, and the self-regular formulation shows strong stability. The implemented code is open-source and is available under the GNU General Public License.

The article shows how the constitutive modeling of concrete has evolved since the initial attempts to characterize the medium cracked as continuous, moving from smeared cracking, damage and microplane models, until the current tendency to design different models according to a single theoretical framework. A generic formulation for smeared cracking models, including fixed and rotational models, as well as degradation in tension and in compression, is provided. Using this formulation, three models are generated by specifying the laws of degradation. A comparative study of models, based on computer simulations of a beam subjected to shear at four points, is presented. The results are compared, between themselves and with experimental results, providing a critical analysis of the models.

A comparison of two microplane constitutive models for quasi-brittle materials

This article presents a comparison of two microplane constitutive models. The basis of the microplane constitutive models are described and the adopted assumptions for the conception of these models are discussed, with regard to: decomposition of the macroscopic strains into the microplanes, definition of the microplane material laws, including the choice of variables that control the material degradation, and homogenization process to obtain the macroscopic quantities. The differences between the two models, with respect to the employed assumptions, are emphasized and expressions to calculate the macroscopic stresses are presented. The models are then used to describe the behavior of quasi-brittle materials by finite element simulations of uniaxial tension and compression and pure share stress tests. The results of the simulations permit to compare the capability of the models in describing the post critical strain-softening behavior, without numerically induced strain localization.

This article presents a software for structural analysis of plates that provides a variety of finite elements, based on the theories of Kirchhoff and Reissner-Mindlin. These theories are briefly discussed, highlighting differences and particularities relevant to software design. The implementation of the system, conducted under the paradigm of object-oriented programming, is then presented through Unified Modelling Language (UML) diagrams that describe the main classes and interfaces used. For purposes of illustration and validation of the resources available, some numerical simulations are presented. Finally, the importance of the system to study the issue and the possibilities of its expansion are discussed.

Elementos finitos de casca do sistema computacional INSANE

This paper presents the shell finite elements of the computer system INSANE (INteractive Structural ANalysis Environment): four-node rectangular and three-node triangular, obtained by combining membrane and bending efforts, based on the Theory of Kirchhoff; a quadrilateral of four, eight and nine nodes that combines membrane, bending and shear efforts, according to the Reissner-Mindlin Theory. After summarizing the characteristics of the elements, the paper presents results of three convergence studies and two practical applications: an arch dam and a conical-cylindrical reservoir. The results are compared with analytical solutions and those obtained with the shell finite element of SAP2000.

This article discusses the use of the generalized continuum theories to incorporate the effects of the microstructure in the nonlinear finite element analysis of quasi-brittle materials and, thus, to solve mesh dependency problems. A description of the problem called numerically induced strain localization, often found in Finite Element Method material non-linear analysis, is presented. A brief historic about the Generalized Continuum Mechanics based models is presented, since the initial work of Voigt (1887) until the more recent studies. By analyzing these models, it is observed that the Cosserat and microstretch approaches are particular cases of a general formulation that describes the micromorphic continuum. After reporting attempts to incorporate the material microstructure in Classical Continuum Mechanics based models, the article shows the recent tendency of doing it according to assumptions of the Generalized Continuum Mechanics. Finally, it presents numerical results which enable to characterize this tendency as a promising way to solve the problem.